Stability analysis and Hopf bifurcation of a fractional order HIV model with saturated incidence rate and time delay
In this paper, a fractional order HIV model with saturated incidence rate and time delay is proposed and analyzed. Firstly, the existence and uniqueness of positive solutions are proved. Secondly, the basic reproduction number and the sufficient conditions for the stability of two equilibriums are o...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824007932 |
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| _version_ | 1846160391158104064 |
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| author | Ruiqing Shi Yihong Zhang |
| author_facet | Ruiqing Shi Yihong Zhang |
| author_sort | Ruiqing Shi |
| collection | DOAJ |
| description | In this paper, a fractional order HIV model with saturated incidence rate and time delay is proposed and analyzed. Firstly, the existence and uniqueness of positive solutions are proved. Secondly, the basic reproduction number and the sufficient conditions for the stability of two equilibriums are obtained. Thirdly, by using time delay as the bifurcation parameter, it is found that Hopf bifurcation may occur when the time delay passes through a sequence of critical values. After that, some numerical simulations are performed to verify the theoretical results. Finally, some discussions and conclusions are listed. |
| format | Article |
| id | doaj-art-4785159463594e86b79e717e64b7e0c5 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-4785159463594e86b79e717e64b7e0c52024-11-22T07:36:10ZengElsevierAlexandria Engineering Journal1110-01682024-12-011087088Stability analysis and Hopf bifurcation of a fractional order HIV model with saturated incidence rate and time delayRuiqing Shi0Yihong Zhang1Corresponding author.; School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030031, ChinaSchool of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030031, ChinaIn this paper, a fractional order HIV model with saturated incidence rate and time delay is proposed and analyzed. Firstly, the existence and uniqueness of positive solutions are proved. Secondly, the basic reproduction number and the sufficient conditions for the stability of two equilibriums are obtained. Thirdly, by using time delay as the bifurcation parameter, it is found that Hopf bifurcation may occur when the time delay passes through a sequence of critical values. After that, some numerical simulations are performed to verify the theoretical results. Finally, some discussions and conclusions are listed.http://www.sciencedirect.com/science/article/pii/S1110016824007932Fractional orderHIV modelSaturated incidence rateStabilityDelayHopf bifurcation |
| spellingShingle | Ruiqing Shi Yihong Zhang Stability analysis and Hopf bifurcation of a fractional order HIV model with saturated incidence rate and time delay Alexandria Engineering Journal Fractional order HIV model Saturated incidence rate Stability Delay Hopf bifurcation |
| title | Stability analysis and Hopf bifurcation of a fractional order HIV model with saturated incidence rate and time delay |
| title_full | Stability analysis and Hopf bifurcation of a fractional order HIV model with saturated incidence rate and time delay |
| title_fullStr | Stability analysis and Hopf bifurcation of a fractional order HIV model with saturated incidence rate and time delay |
| title_full_unstemmed | Stability analysis and Hopf bifurcation of a fractional order HIV model with saturated incidence rate and time delay |
| title_short | Stability analysis and Hopf bifurcation of a fractional order HIV model with saturated incidence rate and time delay |
| title_sort | stability analysis and hopf bifurcation of a fractional order hiv model with saturated incidence rate and time delay |
| topic | Fractional order HIV model Saturated incidence rate Stability Delay Hopf bifurcation |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824007932 |
| work_keys_str_mv | AT ruiqingshi stabilityanalysisandhopfbifurcationofafractionalorderhivmodelwithsaturatedincidencerateandtimedelay AT yihongzhang stabilityanalysisandhopfbifurcationofafractionalorderhivmodelwithsaturatedincidencerateandtimedelay |